serverless functions require the $20/month plan? hmmmm
but lambda will be free for me, although if I use a database it won't be
edit: the usage limits document you posted says there are serverless functions available for hobby/free tier, but the dashboard says the serverless is only available for pro plan. do they mean the serverless GUI is only available?
It seems as if this wasn't clear from the UI. Would you agree? It sounds like you've assumed that it's the entire Serverless Function feature that would not be available.
But reading the docs I’d just copy an example hello world function into my git repository, try to deploy it and check if it works without paying.
Regarding the lambda approach, I personally think lambda functions and especially with the api gateway get too complicated too fast in comparison with a solution like Vercel. I’d definitely recommend an infrastructure as code tool like Terraform if you choose this approach.